The Nationals have shown interest in Garza in the past. Before the Rays traded him to the Cubs before the 2011 season, the Nationals expressed interest in dealing for the right-hander, a person familiar with the situation said. The interest, the person said, was not aggressive, but not insignificant.

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Garza, 29, is eligible to become a free agent this winter. Under the new collective bargaining agreement, any team that trades for Garza would not receive a compensatory draft pick in the event he signed elsewhere.

The price to acquire Garza would be steep. The Baltimore Sun reported the Orioles had offered infielder Jonathan Schoop and pitcher Eduardo Rodriguez for Rodriguez. Both prospects ranked among the Top 100 in baseball coming into the season, according to ESPN’s Keith Law list.